Ultrasound imaging is commonly used for diagnosing breast cancers since it is non-invasive and inexpensive. Breast ultrasound (BUS) image classification is still a challenging task due to the poor image quality and lack of public datasets. In this paper, we propose novel Neutrosophic Gaussian Mixture Models (NGMMs) to more accurately classify BUS images. Specifically, we first employ a Deep Neural Network (DNN) to extract features from BUS images and apply principal component analysis to condense extracted features. We then adopt neutrosophic logic to compute three probability functions to estimate the truth, indeterminacy, and falsity of an image and design a new likelihood function by using the neutrosophic logic components. Finally, we propose an improved Expectation Maximization (EM) algorithm to incorporate neutrosophic logic to reduce the weights of images with high indeterminacy and falsity when estimating parameters of each NGMM to better fit these images to Gaussian distributions. We compare the performance of the proposed NGMMs, its two peer GMMs, and three DNN-based methods in terms of six metrics on a new dataset combining two public datasets. Our experimental results show that NGMMs achieve the highest classification results for all metrics.